Euclid preparation: LXXXVII. Non-Gaussianity of 2-point statistics likelihood: Precise analysis of the matter power spectrum distribution

TL;DR

This paper analyzes the non-Gaussian features of the matter power spectrum distribution using extensive simulations and an analytical framework, highlighting deviations from Gaussianity on nonlinear scales relevant for Euclid.

Contribution

It introduces a detailed analytical approach linking non-Gaussianity to higher-order statistics and assesses survey geometry effects on the power spectrum likelihood.

Findings

Likelihood deviates from Gaussian on nonlinear scales, especially at low redshift.

Pentaspectrum dominates non-Gaussianity at intermediate scales.

Survey geometry and integral constraint increase skewness in measurements.

Abstract

We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generate 100\,000 mock realisations of dark matter density fields in both real and redshift space across multiple redshifts and cosmological models. We derive an analytical framework linking the non-Gaussianity of the power spectrum distribution to higher-order statistics of the density field, including the trispectrum and pentaspectrum. We explore the effect of redshift-space distortions, the geometry of the survey, the Fourier binning, the integral constraint, and the shot noise on the skewness of the distribution of the power spectrum measurements. Our results demonstrate that the likelihood of the estimated matter power spectrum deviates significantly from a Gaussian assumption on nonlinear scales, particularly at low redshift. This departure is primarily driven by the pentaspectrum contribution, which dominates over the trispectrum at intermediate scales. We also examine the impact of the finiteness of the survey geometry in the context of the Euclid mission and find that both the shape of the survey and the integral constraint amplify the skewness.